A resolver is a sensor that outputs an analog signal responsive to a physical rotation angle on the basis of the principle of a transformer. A typical resolver has a stator made of a magnetic material and a rotor made of a magnetic material disposed inside the stator. As an example of such conventional resolvers, FIG. 1 shows a schematic diagram showing a configuration of a one-phase excitation/two-phase output variable reluctance resolver 100 that outputs an analog signal responsive to a physical rotation angle of a rotor by taking advantage of a change of air-gap permeance between the rotor and a plurality of teeth provided on an inner side of a stator.
<Configuration>
As shown in FIG. 1, the illustrated variable reluctance resolver 100 comprises a cylindrical stator 10 and a columnar rotor 20.
On an inner wall of the cylindrical stator 10, a plurality of teeth 11 are arranged at equal intervals in such a way as to come full circle. In a cross section including the arrangement of teeth 11, each tooth 11 protrudes from the inner wall of the stator 10 so that end surfaces 11a of the plurality of teeth 11 facing the rotor 20 form a wall of a virtual cylinder 50. In the following description, a central axis of the virtual cylinder 50 will be referred to as a central axis 12 of the stator 10 or simply as a central axis 12. In FIG. 1, for the sake of simplicity, only some of the teeth and some of the end surfaces are denoted by reference numerals. In the example shown in FIG. 1, the number of teeth 11 is 16.
In this example, the rotor 20 is coupled to a shaft (not shown) that rotates with rotation of a component of a rotating machine, such as a motor or a generator, and rotates about a rotation axis 21. The rotor 20 is disposed to face the teeth 11 in an inner space of the stator 10 so that (1) the rotor 20 is not in contact with any tooth 11 and (2) the rotation axis 21 of the rotor 20 is aligned with the central axis 12 of the stator 10. In this way, the variable reluctance resolver 100 is configured so that the rotor 20 can freely rotate in the inner space of the stator 10.
The outer periphery of the rotor 20 is shaped so that (1) the rotor 20 does not come into contact with any tooth 11 when the rotor 20 is rotating and (2) the outer periphery of the rotor 20 gives the changes of sine or cosine wave-like mx cycles to the air-gap permeance between the teeth 11 and the rotor 20 in a range of one circle of the outer circumference of the rotor 20, where mx represents the drive number of the variable reluctance resolver 100. More specifically, the shape of the outer periphery of the rotor 20 is expressed by the following expression (1), where for convenience, in a vertical cross section of the rotor 20 taken at an arbitrary point along the direction of the rotation axis 21 of the rotor 20, the distance from the rotation axis 21 to an arbitrary point on the outer periphery of the rotor 20 is expressed by a radius r of a circular polar coordinate system having a pole (which is equivalent to the origin of an orthogonal coordinate system) through which the rotation axis 21 of the rotor 20 passes, and the angle formed around the pole by an arbitrary fixed ray (polar axis) on the circular polar coordinate system and the radius r is expressed by a polar angle σ. In this expression, mx denotes the drive number (that is, a pole pair number of the rotor), r0 denotes a reference radius, δ0 denotes a width of the air gap between the virtual cylinder 50 and the rotor 20 at a polar angle σ=π/2mx [rad], δ1 denotes a width of the air gap between the virtual cylinder 50 and the rotor 20 at a polar angle σ=0 [rad], and α=(δ0/δ1)−1 denotes a gap change rate (0<|α|<1). The reference radius r0 is a radius that prescribes the outer circumference of the rotor and is set to be somewhat larger than δ0/(1−|α|). Typically, the distance from the rotation axis 21 of the rotor 20 to the end surface 11a of the teeth 11 (that is, the radius of the virtual cylinder 50) is used as the reference radius r0. The rotor 20 shown in FIG. 1 is a rotor with mx=2.
                    r        =                                            r              0                        -                                          δ                0                                            1                +                                                      (                                                                                            δ                          0                                                                          δ                          1                                                                    -                      1                                        )                                    ⁢                                      cos                    ⁡                                          (                                                                        m                          x                                                ⁢                        σ                                            )                                                                                                    =                                    r              0                        -                                          δ                0                                            1                +                                  α                  ⁢                                                                          ⁢                                      cos                    ⁡                                          (                                                                        m                          x                                                ⁢                        σ                                            )                                                                                                                              (        1        )            
<Coil Configuration for Magnetic Circuit>
An exciting coil 15 is wound around each tooth 11 with a predetermined number of turns and in a predetermined winding direction, and these exciting coils 15 are connected in series with each other. An alternating-current voltage Ve from an exciting power supply (not shown) is applied to a circuit part formed by the series connection of the exciting coils 15. The number of turns and the winding direction of the exciting coil 15 of each tooth 11 are determined so that a sine wave-like or cosine wave-like exciting magnetic flux distribution occurs when the alternating-current voltage Ve is applied. To achieve a good exciting magnetic flux distribution with less distortion, the exciting coils 15 of adjacent two teeth 11 are preferably wound in the opposite directions. More specifically, the number of turns and the winding direction of the exciting coil 15 wound around the tooth 11 that corresponds to a mechanical angle ξ are given by Te which is expressed by the following expression (2), where me denotes the pole pair number in a magnetic flux distribution formed by the exciting coils 15, TEmax denotes the reference number of turns of each of the exciting coils 15, and the mechanical angle ξ denotes an angle around the central axis 12 formed by a reference tooth 11 (referred to as a reference tooth 11S, hereinafter) arbitrarily selected from among the plurality of teeth 11 and another arbitrary tooth 11. That is, the number of turns is |Te|, and the winding direction is a clockwise direction when the polarity of Te is positive and a counterclockwise direction when the polarity of Te is negative. The “clockwise” and “counterclockwise” used herein are directions defined on the assumption that the teeth 11 are viewed from the central axis 12 (the same holds true for the following description). The mechanical angle ξ is 0 [rad](ξ=0 [rad]) at the position of the reference tooth 11S. When the total number of teeth 11 is N, me=N/2. In FIG. 1, for the sake of simplicity, only some of the exciting coils are denoted by reference numerals.Te=TE max cos(meξ)  (2)
Furthermore, two detecting coils of different phases are wound around each tooth 11. One of the detecting coils will be referred to as a cosine-phase coil 17, and the other detecting coil will be referred to as a sine-phase coil 19. The cosine-phase coils 17 are connected in series with each other, and the sine-phase coils 19 are also connected in series with each other.
The number of turns and the winding direction of the cosine-phase coil 17 wound around each tooth 11 are set so that “mx cycles of cosine wave-like output voltage occur in the circuit part formed by the series connection of the cosine-phase coils 17 in a range of one circle of the inner circumference of the stator 10 (that is, in a range of the mechanical angle between 0 [rad] and 2π [rad])” on the basis of the polarity of the exciting coil 15. More specifically, the number of turns and the winding direction of the cosine-phase coil 17 wound around the tooth 11 corresponding to the mechanical angle ξ are given by Tc expressed by the following expression (3), where the number of turns and the winding direction of the exciting coil 15 wound around the tooth 11 corresponding to the mechanical angle ξ are given by Te which is expressed by the expression (2), ms denotes the pole pair number in a magnetic flux distribution formed by the detecting coils, and TSmax denotes the reference number of turns of each of the detecting coils. That is, the number of turns is |Tc|, and the winding direction is the clockwise direction when the polarity of Tc is positive and the counterclockwise direction when the polarity of Tc is negative. To be more strict, no cosine-phase coil 17 is wound around the tooth 11 that corresponds to the mechanical angle ξ with which a relation |Tc|=0 holds. In FIG. 1, for the sake of simplicity, only some of the cosine-phase coils are denoted by reference numerals.Tc=TS max cos(msξ)  (3)
The number of turns and the winding direction of the sine-phase coil 19 wound around each tooth 11 are set so that “mx cycles of sine wave-like output voltage occur in the circuit part formed by the series connection of the sine-phase coils 19 in a range of one circle of the inner circumference of the stator 10 (that is, in a range of the mechanical angle between 0 [rad] and 2π [rad])” on the basis of the polarity of the exciting coil 15. More specifically, the number of turns and the winding direction of the sine-phase coil 19 wound around the tooth 11 corresponding to the mechanical angle ξ are given by Ts expressed by the following expression (4), where the number of turns and the winding direction of the exciting coil 15 wound around the tooth 11 corresponding to the mechanical angle ξ are given by Te expressed by the expression (2), ms denotes the pole pair number in a magnetic flux distribution formed by the detecting coils, and TSmax denotes the reference number of turns of each of the detecting coils. That is, the number of turns is |Ts|, and the winding direction is the clockwise direction when the polarity of Ts is positive and the counterclockwise direction when the polarity of Ts is negative. To be more strict, no sine-phase coil 19 is wound around the tooth 11 that corresponds to the mechanical angle ξ with which a relation |Ts|=0 holds. In FIG. 1, for the sake of simplicity, only some of the sine-phase coils are denoted by reference numerals.Ts=TS max sin(msξ)  (4)
With the variable reluctance resolver 100, the rotor 20 is not provided with any coil.
With the configuration described above, when the rotor 20 rotates in a variable magnetic field induced by an alternating current flowing through the exciting coils 15, a cosine-phase output voltage Vcos having a voltage amplitude responsive to the rotation angle of the rotor 20 occurs in the circuit part formed by the cosine-phase coils 17, and a sine-phase output voltage Vsin having a voltage amplitude responsive to the rotation angle of the rotor 20 occurs in the circuit part formed by the sine-phase coils 19. The rotation angle of the rotor 20 can be detected from the two output voltage of the two phases.
Resolvers like the resolver described above are disclosed in Patent literature 1 (Japanese Patent Application Laid-Open No. 2013-53890) and Patent Literature 2 (Japanese Patent Application Laid-Open No. H10-239010).
With the configuration described above, a mismatch between the rotation axis 21 of the rotor 20 and the central axis 12 of the stator 10 (see FIG. 2) has an effect on the air gap between the teeth 11 and the rotor 20. As a result, the air-gap permeance between the teeth 11 and the rotor 20 does not change in an ideal sine wave form or an ideal cosine wave form. The change of the air-gap permeance occurs in the voltage amplitude of each of the two output voltages of the two phases, so that any disturbance in the change of the air-gap permeance immediately causes an error of the detected rotation angle. That is, a mismatch between the rotation axis 21 of the rotor 20 and the central axis 12 of the stator 10 causes deterioration of precision of detection of the rotation angle.
Although a variable reluctance resolver has been described as an example, a similar problem occurs in resolvers with a common configuration, such as a brushless resolver.